Mahmoud Ahmad­inejad claimed a victory that many find difficult to believe: 64% of the vote on a turnout of 84% in Iran's election. The provincial breakdown of the results – obtained by the University of St Andrews and Chatham House from Iran's ministry of interior – show some statistics that are even more surprising.

The surprises include voter turnouts of up to 100%, and the apparent defection of huge numbers of former reformist voters who suddenly changed their minds and voted conservative. Turnout may have been high across the board, but the just over 100% recorded in the conservative strongholds of Yazd and Mazandaran is particularly striking. Four other provinces recorded turnouts of over 90%. In a country with a long history of using the identity documents of the deceased to cast extra ballots, this could be of concern to the reformists.

Ahmadinejad claims to have gathered 13m votes more than all three conservative candidates combined managed in 2005. If true, this would be the biggest increase in a vote since the birth of the Islamic Republic, and conveniently bigger than that achieved by the reformist winner in 1997, Mohammad Khatami. This is odd. The major reformist organisations boycotted the 2005 poll, which Ahmadinejad won, and so the re-entry of these voters might be expected to boost the reformist challenger Mir Hossein Mousavi. Not so, apparently.

By contrast, the conservative camp in 2005 organised a secret campaign to mobilise their core vote for Ahmadinejad. While they may have organised even more effectively this time, with four years to prepare and greater resources at their disposal, to have increased their vote by 113% would be quite spectacular.

So where did these 13m votes come from? Our analysis broke down the 2009 vote in each province into voters who had voted for reformists, the sole centrist and conservatives respectively, and those who had not voted at all. The suggestion that Ahmadinejad's success came from a groundswell of previously unengaged conservative voters was not held out by the data. We found that there was no real correlation between the increase in participation in a province, and the swing to Ahmadinejad.

For the numbers to add up, in 10 out of Iran's 30 provinces, Ahmadinejad would have had to win the votes of all those who did not vote in 2005, all those who voted for the centrist Hashemi Rafsanjani in 2005, and up to 44% of those who voted for reformist candidates that year. For anyone who has experienced the polarisation of Iranian politics in the last decade, this is hard to believe.

Instead, it seems Ahmadinejad recorded many of his greatest victories in rural, often ethnic minority, provinces that formerly supported the reformist cleric Mehdi Karrubi. Rural and ethnic minority provinces (contrary to much popular opinion in the west) have traditionally voted against conservatives. Most notable of these was Karrubi's home province, Lorestan, where his 2005 tally of 55.5% was cut to just 4.6%, with an overall increase of 296% in the conservative vote. In a province with a long history of supporting ethnic Lors like Karrubi, this is even more surprising. Ilam, Khuzestan and the crucial province of Fars all saw huge swings from the cleric to Ahmadinejad.

The breakdown of the votes is not a smoking gun, it does after all come from the same ministry of interior run by Ahmadinejad's former campaign manager, which conducted the count. However, it shows that even the official ­version of events makes some claims that are difficult to swallow.

• This article was amended on 20 May 2014 to remove details of an author for personal reasons.